The present invention is directed to an acoustic method and apparatus for measuring the quantity and installed density of thermal insulation and more specifically to the arrangement of one or more acoustic transducers and/or reflecting means in or adjacent the insulation for directing acoustic waves through the insulation to measure the attenuation and/ or phase shift of the acoustic waves passing through the insulation.
When a sound wave passes through a porous material, such as a loose-fill insulation, the sound wave undergoes both amplitude attenuation and a phase shift that depend on the nature of the material and the frequency of the sound. For example the sound attenuation of fibrous materials is dependent upon the material itself, the distribution of fiber diameters, the surface condition of the fiber, the binder, the bulk density, and the type and density of the gas filling the pores of the material. These same factors also affect the thermal conductivity of fibrous material.
These factors are related in the following way. The sound pressure, p, associated with a plane acoustic wave traveling in the positive x-direction in a porous medium can be expressed as EQU p(x,t)=p(O,t) exp (-.gamma.x),
where t is time and the complex propagation coefficient .gamma. can be written as EQU .gamma.=.alpha.+j.beta.,
where the real part is called the attenuation coefficient and the imaginary part .beta. is the phase coefficient. The attenuation coefficient, which is a property of the porous medium and of the frequency of the sound wave, determines the decay of the sound intensity with distance in the medium. The phase coefficient, which also is a property of the medium and the sound frequency, determines the speed of sound propagation through the medium.
If the dependence of the attenuation coefficient on the bulk density or the porosity of the medium is known, a measurement of the sound attenuation over a given distance enables calculation of the density. Similarly, if the dependence of the phase coefficient or the sound speed on the density is known, a measurement of the speed of sound enables calculation of the density of the medium.
For randomly oriented fibrous material, the attenuation coefficient is known empirically to depend upon the bulk density, .rho., of the insulation, the average fiber diameter, d, and the sound frequency, f, according to the approximate relationship ##EQU1## where .alpha..sub.0 is a reference attenuation coefficient corresponding to the values .rho.=.rho..sub.0, d=d.sub.0, and f=f.sub.0. The exponents 0.9, 1.2, and 0.4 vary somewhat and should be determined empirically for a given material. For a given type of fibrous insulation, the average fiber diameter is fixed. Since the sound frequency can also be fixed experimentally, this equation reduces to a simple relationship between the attenuation coefficient and the bulk density of the insulation. Similar types of relationships can be developed for types of thermal insulation other than fibrous materials.
For randomly oriented fibrous material, the phase coefficient is known empirically to be given approximately by ##EQU2## where .beta..sub.0 is a reference phase coefficient and c is the acoustic wave speed in air. The exponents should be confirmed experimentally. For a given material (i.e., a given fiber diameter) and sound frequency, this equation provides a simple relationship between the phase coefficient and the bulk density of the insulation.
It is well known that the effective thermal conductivity of a given loose-fill insulating material depends upon the bulk density of that material. For mineral fiber insulations, the effective thermal conductivity, of relatively thick insulation is related to the bulk density, .rho., of the material by an equation of the form ##EQU3## where A, B, and C are constants, A representing the thermal conductivity of the gas (air) filling the insulation, B.rho. representing heat conduction through the fibers and the interaction of that conduction with the surrounding gas, and C/.rho. representing the radiative heat transfer through the porous insulation. If this relationship is known for a given type of insulation, and the bulk density is determined from experimental measurements of the attenuation coefficient and/or the phase coefficient the thermal conductivity can be computed.
A method and apparatus for measuring characteristic features of fibrous materials is disclosed in U.S. Pat. No. 4,481,820, to Thomann, granted Nov. 15, 1984. The method disclosed in this patent relates to the measurement of fibrous materials such as slivers and rovings by ultrasonics. In a suitable arrangement of a sound source and a sound pickup with the fibrous material disposed therebetween, only those sound waves arrive at the sound pickup which have penetrated the fibrous material. All lagging disturbing signals which are generated by reflections and interferences are suppressed by a pulsed operation of the sound source and by the corresponding gating of the sound pickup, as a result of which, a value to be measured, namely, the quantity of fibers present at any time in the measuring data, is substantially free from disturbing influences. In order to accomplish this, the fibrous material, in particular a sliver or the like, is guided by lateral boundary surfaces such that all the sound waves are forced to penetrate the fibrous volume in order to arrive at the pickup from the source. The lateral boundary surfaces are preferably formed by parallel plates, the magnitude of compression being selected such that the fibrous material rests closely against the plate. Therefore such a method and apparatus would not be suitable for the measurement of the quantity and density of installed thermal insulation.
Post installation measurement of insulation layers is necessary to ascertain that the correct amount of insulation has in fact been installed. The widely used cookie cutter method has been found unsatisfactory by regulatory agencies for several reasons. This method entails measuring the thickness and cutting out samples of the insulation from representative locations in an attic or other insulated region, placing them in bags, taking them outside of the attic, weighing them and finally restoring the specimens to the places, whence they were originally removed. The weight, thickness and dimension of the removed specimens yield the volume and density of the insulation which can be used to estimate the insulating value or thermal resistance from a previously established relationship for a given insulating material. However many problems are associated with this method, such as difficulties encountered in entering the attic space through a small scuttle hole, walking over ill-defined attic wood frames which are often hidden beneath several inches of thick loose-fill insulation, and removing reproducible and well defined specimens and restoring them to the spots from which they were removed. It has been estimated that the error associated with this method is fifteen to twenty percent.